An amusement park currently charges the same price for each ticket of

Hey! this is how i got the answer.

160/x = (160/x) +12

Solve the equation and we will get x= -8 or x=5, the price of the ticket cannot be negative so x=5 is the correct answer.
B

Answer = B = 5

Price ............. Quantity .................. Total

a ...................... \(\frac{160}{a}\) ..................... 160 (Assume price = "a")

a+3 ................... \(\frac{160}{a} - 12\) ............... 160 (Price increased by 3, sales decline by 12)

Solving the equation

\((a+3)* (\frac{160}{a} - 12) = 160\)

\(a^2 + 3a - 40 = 0\)

a = 5

Plug in is the best approach for this question to save time. Answer is B.

Let price be p & no. of tickets be n.

p*n = 160
(p+3)*(n-12) = 160

If price is 3, n = 160/3, n is not a whole no. , so 3 is not the answer
If price is 5, n=32 from 1st eqn...checking with 2nd equation 8*(n-12) = 160 -> 8n = 256 -> n=32. Price $5 satisfies both equations.

Hence answer B.

Official Solution:

An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by \($3\), 12 fewer tickets could be bought for \($160\), excluding sales tax. What is the current price of each ticket?

A. \($3\)
B. \($5\)
C. \($8\)
D. \($20\)
E. \($32\)

The question asks us to determine the current price of each ticket of admission.

If we let \(p\) equal the current price per ticket, and \(n\) equal the number of tickets that can be bought for \($160\), we can set up some equations. First, we know that \(pn = 160\).

Second, we are told that if \(p\) is increased by 3, then 12 fewer tickets can be bought with \($160\). This equation also expresses how many tickets can be bought for \($160\), giving us: \((p + 3)(n - 12) = 160\).

Solve the first equation for \(n\), giving: \(n = \frac{160}{p}\).

Substitute this value for \(n\) into the second equation, solving for \(p\):

\((p + 3)(\frac{160}{p} - 12) = 160\)

Multiply both sides by \(p\) to get rid of the fraction: \((p + 3)(\frac{160}{p} - 12)p = (p + 3)(160 - 12p) = 160p\).

Multiply through to get rid of the parentheses: \(160p - 12p^2 + 480 - 36p = 160p\).

Combine like terms: \(124p - 12p^2 + 480 = 160p\). Set the equation equal to 0: \(0 = 12p^2 + 36p - 480\).Divide both sides by 12: \(0 = p^2 + 3p - 40\).

Factor: \(0 = (p - 5)(p + 8)\).

Therefore, \(p = 5\) or \(p = -8\). Since the the price cannot be negative, \(p = 5\).

Answer: B.

60-second approach: Use the answer choices.

The $160 total stays constant, but the ticket price goes up by $3.

Add $3 to each answer, and four answers are eliminated very quickly: A, C, D, and E.

The new prices for those four choices do not divide evenly into $160.*
Total price / price per ticket = # of tickets, which will not be a whole integer at new price for options A, C, D, and E.

A. ($3-->$6)
C. ($8-->$11)
D. ($20-->$23)
E. ($32-->$35)

That leaves B. If brave, mark and move on. If not (raises hand), check.

$160/$5 = 32 tickets sold

$160/$8 = 20 tickets sold

Higher price = 12 fewer tickets. Correct.

Answer B

* Ticket prices for four answers do not divide evenly into 160.
-- C and D (11 and 23). Fairly obvious, but primes 11 and 23 do not divide evenly into 160.
Primes 11 and 23 are NOT factors of 160: (16*10) = (2*8*10)=(2*8*2*5). No 11 or 23.
-- A? If uncertain about A, add digits of 160; not divisible by 3, so not divisible by 6.
-- For E, $35 * 2 = 70, and $70 doubled is $140. The extra is $20 (160-140). That won't work; you can't divide 20 by 35 evenly.

An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by $3, 12 fewer tickets could be bought for $160 excluding sales tax. What is the current price of each ticket?

Let N be the no. of tickets currently brought and P be the price per ticket,

According to the given question
=> NP = (N-12)(P-3) = 160
=> NP -3N-12P+36 = 160
=>3N+12P-36=0

Substituting N = 160/P

=> 480 + 12P^2 - 36P =0
=>P^2 - 3P + 40 =0
=> (P-5)(P+8)

=> P =5

Hence B